The labour ministry declared a three-day holiday for companies and establishments in the private sector, state news agency ONA reported.
The central bank, meanwhile, issued a circular announcing a three-day holiday starting on Sunday for money exchange houses, banks, finance and leasing companies in Dhofar.
Cyclone Mekunu hit southern Yemen and the coast of neighbouring Oman over the weekend, resulting in several fatalities.
Salalah Port Services Co said that operations at the port had been halted because of the damage caused by the cyclone and that it would take a minimum of 72 hours to "make the port safe".
Sembcorp Salalah Water and Power Co, which operates an electricity generation and seawater desalination plant in Oman, said its water production plant had been shut down temporarily owing to rough seas because of a tropical storm.